The book I'm following for Strength of materials states that, in a beam with symmetric cross section (about the plane of bending) and in pure bending, the moment of cross sectional area about the neutral axis is zero, i.e.
$$\int_A y\,dA=0$$
where $y$ is the perpendicular distance of an area $dA$ from the neutral axis.
The book then says that, this could only happen when the neutral axis passes through the centroid of section, and I don't understand why.
I have a feeling this might be very trivial to ask, but please bear with me.